nple (nathanple)

Race #50

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Official speed 96.71 wpm (107.21 seconds elapsed during race)
Without ending ping 96.92 wpm (236 ms delay sending score to TypeRacer’s server)
Timerless 97.58 wpm (719 ms elapsed before first character typed; 106.25 seconds elapsed during race)
Timerless minus one 97.47 wpm, ignoring the first character typed
Race Start October 11, 2023 4:33:38pm UTC
Race Finish October 11, 2023 4:35:25pm UTC
Outcome Win (1 of 3)
Opponents 2. tysie01 (92.37 wpm)
Accuracy 97.9%
Points 261.12
Text #4940058 (Length: 864 characters)

Calculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does the speed of a falling object change as a function of time? How does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but for now we use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Characters typed Calculus is a tool that helps us understand how a change in one qunaanittity is related to a change in another. How does the speed of a falling object change as a function of time? How doe sthe s the level of water in a barrel change as a function of the amount of liquid ppoured into it? We see change occuring iring in nearly everything we observe in teh he world and universe, adn nd powerful modern instruments help us see more and more. In this section we introduce the ideas of eaaverage and instantaneous rates of change, and show that they are clseosely related to the slop eo e of a curve at a point P on the curve. We tigive precise developments of these important concepts in the next chapter, but for now we suuse an informal approach so you will see now thow they lead natruurally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calcullususus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 719 111 104 99 107 108 95 141 16 140 122 65 107 80 91 47 141 171 109 110 49 44 95 31 141
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 114 125 202 236 108 251 114 90 151 73 50 171 41 148 112 154 121 131 78 93 61 78 52 95 72
Character c h a n g e i n o n e q u n a -a -n a n i t -t
Milliseconds 127 90 65 106 82 105 62 95 62 63 97 127 31 60 174 55 100 63 391 78 94 94 127 30 318
Character -i t i t y i s r e l a t e d t o a c h a
Milliseconds 104 143 47 155 93 92 129 78 65 107 53 105 266 97 126 201 78 93 63 63 77 94 110 80 73
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 98 78 85 77 105 48 93 78 91 60 144 109 94 52 122 77 172 97 77 170 144 79 61 94 9
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 120 27 76 48 129 105 80 140 174 110 90 101 90 41 93 91 112 48 156 63 78 82 0 185 201
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 179 106 73 190 78 123 94 94 112 77 77 123 224 106 85 103 78 96 89 62 96 189 74 17 91
Character o f t i m e ? H o w d o e s t h e - -e
Milliseconds 77 96 94 80 108 129 107 141 210 77 259 299 142 82 193 51 122 78 27 101 33 33 61 293 142
Character -h -t -s - s t h e l e v e l o f w a t e r
Milliseconds 103 118 164 115 218 106 132 62 56 60 109 98 80 138 64 74 111 96 36 126 126 50 99 71 52
Character i n a b a r r e l c h a n g e a s a f
Milliseconds 92 76 64 32 76 199 113 148 185 62 63 82 96 99 35 129 96 62 127 402 73 111 98 82 103
Character u n c t i o n o f t h e a m o u n t o f
Milliseconds 73 64 50 216 11 79 64 82 138 112 143 98 48 58 76 109 113 85 95 79 62 143 63 103 65
Character l i q u i d p p -p o u r e d i n t o i t ?
Milliseconds 147 60 153 86 136 100 112 384 127 375 203 68 86 204 194 58 78 62 93 78 48 123 81 211 74
Character W e s e e c h a n g e o c c u r i n g i -i
Milliseconds 219 109 171 285 78 169 50 136 63 16 172 63 77 113 207 93 160 60 126 93 52 70 72 106 288
Character - -g -n -i r i n g i n n e a r l y e v e r y t
Milliseconds 95 133 155 161 122 144 49 77 53 112 82 53 156 82 92 83 60 93 60 94 130 135 48 110 157
Character h i n g w e o b s e r v e i n t e h - -h
Milliseconds 93 82 118 35 85 105 66 71 198 146 150 129 70 202 92 120 74 62 59 84 78 0 234 280 116
Character -e h e w o r l d a n d u n i v e r s e , a
Milliseconds 115 207 81 91 112 79 264 223 96 92 97 99 72 80 170 70 128 66 96 81 91 106 111 69 171
Character d n - -n -d n d p o w e r f u l m o d e r n
Milliseconds 115 16 253 252 116 112 198 112 95 117 55 174 60 65 177 56 115 97 164 78 97 175 64 73 103
Character i n s t r u m e n t s h e l p u s s e e m
Milliseconds 137 75 56 71 142 96 149 177 116 101 93 100 82 156 97 158 96 166 94 94 141 111 190 93 79
Character o r e a n d m o r e . I n t h i s s e c
Milliseconds 77 63 47 79 109 64 94 91 142 63 76 30 127 32 187 84 61 126 78 113 176 71 132 86 149
Character t i o n w e i n t r o d u c e t h e i d e
Milliseconds 201 79 62 81 78 109 68 101 108 80 78 147 112 177 115 201 61 154 44 125 0 119 94 66 202
Character a s o f e a -a -e a v e r a g e a n d i n s
Milliseconds 70 145 44 109 92 46 139 76 359 126 49 84 108 128 111 133 92 58 211 29 314 146 177 56 76
Character t a n t a n e o u s r a t e s o f c h a n g
Milliseconds 79 92 85 90 221 128 114 225 102 125 46 126 93 126 50 129 83 67 93 46 139 85 69 251 108
Character e , a n d s h o w t h a t t h e y a r e
Milliseconds 110 85 72 109 126 94 76 396 62 94 111 46 170 63 32 92 47 119 55 108 48 107 68 66 90
Character c l s e -e -s o s e l y r e l a t e d t o t
Milliseconds 29 173 98 156 61 359 97 206 82 46 97 133 78 148 55 108 138 79 121 174 78 148 10 373 145
Character h e s l o p e o - -o -e - e o f a c u r
Milliseconds 82 60 67 152 80 124 186 82 95 116 112 240 98 99 153 351 99 137 94 49 97 80 155 96 92
Character v e a t a p o i n t P o n t h e c u
Milliseconds 241 110 112 129 95 92 74 96 127 49 191 66 62 78 167 160 201 96 95 74 62 48 73 130 104
Character r v e . W e t i -i -t g i v e p r e c i s e
Milliseconds 107 176 96 79 60 526 277 103 162 107 314 111 157 97 92 111 92 105 96 65 181 110 513 77 132
Character d e v e l o p m e n t s o f t h e s e i m p
Milliseconds 289 158 131 108 58 145 163 174 116 95 122 74 94 74 68 53 113 50 108 78 116 77 131 58 114
Character o r t a n t c o n c e p t s i n t h e n e
Milliseconds 52 25 69 74 76 114 154 157 62 60 82 62 205 140 125 78 93 78 46 109 90 17 128 124 79
Character x t c h a p t e r , b u t f o r n o w w
Milliseconds 177 182 62 158 90 110 77 133 132 77 64 52 150 62 78 190 139 65 91 31 129 75 78 64 140
Character e s u -u -s u s e a n i n f o r m a l a p p
Milliseconds 47 126 138 15 469 110 187 139 103 24 315 90 109 143 79 110 93 97 109 120 99 94 110 71 102
Character r o a c h s o y o u w i l l s e e n o w
Milliseconds 108 109 268 140 93 125 130 89 124 145 112 72 63 91 77 127 155 96 128 58 192 78 141 62 129
Character t -t - -w -o -n h o w t h e y l e a d n a t r
Milliseconds 30 124 232 106 153 250 140 778 105 84 59 100 47 109 63 80 365 89 34 109 74 176 87 69 168
Character u -u -r u r a l l y t o t h e m a i n i d e
Milliseconds 141 266 111 174 78 67 90 94 126 51 156 141 93 112 76 76 79 63 95 62 95 47 95 92 140
Character a o f t h i s c h a p t e r , t h e l i
Milliseconds 60 146 87 109 78 139 46 46 93 32 192 90 158 62 157 263 50 106 45 194 95 108 65 300 48
Character m i t . T h e i d e a o f a l i m i t
Milliseconds 92 126 142 79 76 144 58 94 111 94 79 156 47 157 88 133 91 78 94 210 103 79 118 90 113
Character p l a y s a f o u n d a t i o n a l r o l e
Milliseconds 132 61 68 105 121 66 111 66 187 63 64 98 0 126 173 101 57 54 119 91 78 144 96 148 78
Character t h r o u g h o u t c a l c u l l u s -s -u u s
Milliseconds 95 94 100 80 64 32 88 42 144 47 104 28 238 123 133 141 97 124 127 71 132 285 113 218 127
Character -s -u -l u s .
Milliseconds 187 109 128 201 136 95
WPM Timing
Seconds WPM
2.14 83.95
4.29 92.34
6.43 100.74
8.58 95.14
10.72 95.14
12.86 101.67
15.01 105.54
17.15 106.34
19.3 107.58
21.44 102.98
23.59 100.74
25.73 103.07
27.87 103.32
30.02 104.74
32.16 102.98
34.31 102.14
36.45 99.09
38.59 101.05
40.74 99.56
42.88 99.06
45.03 97.54
47.17 98.45
49.32 98.31
51.46 99.81
53.6 100.07
55.75 99.66
57.89 99.7
60.04 99.94
62.18 100.55
64.32 99.99
66.47 100.02
68.61 98.29
70.76 98.53
72.9 98.27
75.04 97.22
77.19 96.85
79.33 98.02
81.48 98.38
83.62 98.73
85.77 98.08
87.91 98.28
90.05 97.14
92.2 96.44
94.34 96.03
96.49 96.88
98.63 96.85
100.77 97.29
102.92 97.82
105.06 98.34
107.21 96.71